The □b-heat equation on quadric manifolds

Abstract

In this article, we give an explicit calculation of the partial Fourier transform of the fundamental solution to the □b -heat equation on quadric submanifolds M ⊂ ℂn ×m . As a consequence, we can also compute the heat kernel associated with the weighted ∂̄ -equation in ℂn when the weight is given by exp(-φ(z,z) λ) where φ:ℂn ×ℂ n →ℂm is a quadratic, sesquilinear form and λ ∈ ℝm . Our method involves the representation theory of the Lie group M and the group Fourier transform.

abstract = "In this article, we give an explicit calculation of the partial Fourier transform of the fundamental solution to the □b -heat equation on quadric submanifolds M ⊂ ℂn ×m . As a consequence, we can also compute the heat kernel associated with the weighted {\=∂} -equation in ℂn when the weight is given by exp(-φ(z,z) λ) where φ:ℂn ×ℂ n →ℂm is a quadratic, sesquilinear form and λ ∈ ℝm . Our method involves the representation theory of the Lie group M and the group Fourier transform.",

N2 - In this article, we give an explicit calculation of the partial Fourier transform of the fundamental solution to the □b -heat equation on quadric submanifolds M ⊂ ℂn ×m . As a consequence, we can also compute the heat kernel associated with the weighted ∂̄ -equation in ℂn when the weight is given by exp(-φ(z,z) λ) where φ:ℂn ×ℂ n →ℂm is a quadratic, sesquilinear form and λ ∈ ℝm . Our method involves the representation theory of the Lie group M and the group Fourier transform.

AB - In this article, we give an explicit calculation of the partial Fourier transform of the fundamental solution to the □b -heat equation on quadric submanifolds M ⊂ ℂn ×m . As a consequence, we can also compute the heat kernel associated with the weighted ∂̄ -equation in ℂn when the weight is given by exp(-φ(z,z) λ) where φ:ℂn ×ℂ n →ℂm is a quadratic, sesquilinear form and λ ∈ ℝm . Our method involves the representation theory of the Lie group M and the group Fourier transform.